In this correspondence a new routing cost function is defined which is a function of local blockage density in addition to path length. A parameter a specifies the degree to which density is to influence the cost. The use of such a cost function results in what we refer to as a density router. The classical Lee router is a special case of the density router with a equal to 0. We present four performance measures (two of which are based on the density of blockages) for comparing the performance of the classical Lee router with that of the density router. It is experimentally determined that a value of a of about 1.25 optimizes our cost function for the density router when evaluated according to each of the four performance measures and for the board model assumed.